Modern statistical theory concerns the estimation of objects in complex parameter spaces, for example a space
of regression functions with a huge number of variables, or a collection of convex sets in image analysis, etc. A
key point is the way one describes smoothness.
For example, smoothness may sparsity, e.g. in the number of
coefficients in a wavelet expansion,
or the dimension of a manifold. A main theme in this workshop
is adapting to unknown smoothness, using penalty based methods
which are computationally feasible for high-dimensional problems.
There will be many connections
with analysis and approximation theory.
There are also quite a few further apparent relations with other branches
of mathematics.
For example, concentration inequalities
from probability theory are nowadays a main statistical
tool. As another example, statistics uses and extends various techniques
from optimization theory
(e.g., convex optimization, exponential weighting, interior point methods).
Moreover, from the algorithmic point of view, statistical problems have clear relations
with e.g. compressing and learning algorithms in computer science.
There will be two subthemes. The first is "Graphical modeling and causal inference",
with important connections to the theory of sparse (random) graphs, discrete optimization
including randomized algorithms, and sparse approximation.
The second subtheme is
"Statistical and stochastic modeling in biology", inspired by the
high-throughput technology in molecular biology or bio-medicine, and
systems biology, where often advanced mathematical modeling or statistical
signal extraction are needed for meaningful complexity reduction or efficient
extraction of information.